Math 131: Syllabus

For the weekly schedules, see the Schedule.

Introduction – What is calculus?

Chapter 2 – Limits and derivatives

    2.1   The tangent and velocity problems
    2.2   The limit of a function
    2.3   Calculating limits using the limit laws
    2.4   The precise definition of a limit
    2.5   Continuity
    2.6   Limits at infinity; horizontal asymptotes
    2.7   Derivatives and rates of change
    2.8   The derivative as a function

Chapter 3 – Differentiation Rules

    3.1   Derivatives of polynomials and exponential functions;
            see also 1.5
    3.2   The Product and Quotient Rules
    3.3   Derivatives of trigonometric functions
    3.4   The Chain Rule
    3.5   Implicit differentiation
    3.6   Derivatives of logarithmic functions; see also 1.6
    3.7   Rates of change in the natural and social sciences
    3.8   Exponential growth and decay
    3.9   Related rates
    3.10 Linear approximations and differentials

Chapter 4 – Applications of Differentiation

    4.1   Maximum and minimum values
    4.2   The Mean Value Theorem
    4.3   How derivatives affect the shape of a graph
    4.4   Indeterminate forms and L’Hospital’s Rule
    4.7   Optimization problems
    4.8   Newton’s Method
    4.9   Antiderivatives

Chapter 5 – Integrals (introduction)

    5.1  Areas and distances
    5.2  The definite integral and Riemann sums

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